Question

D Chapter 15 Problem Set Suppose you are planning a study that will est the following one-tailed hypotheses: To evaluate the power of your study, you consider a specific alternative hypothesis, μ-Ha, where μ.> μ。. The following sketch shows two overlapping sampling distributions of X-one when Ho is true (and H1 is false), the other when Hy is true (and Ho is false). The distribution on the left has a mean of yo and represents the sampling distribution of X if the null hypothesis (Ho) is true. The distribution on the right has a mean of ua and represents the sampling distribution of X if the alternative hypothesis (H1) is true. Но На Note that various areas under the curves are shaded in blue, red, gray, and horizontal lines. The area shaded in red is the level of significance a. The first column of the following table describes events that could occur when you conduct your hypothesis test. For each of these events, select the value, expressed in o and B, in the second column that matches the probability of that event. Recall that a is the probeblity of a Type I orror, that is, rejectino the null hypothesis when it is true B s the probability of a Type ll error, thet is, not rejecting the nul hypothesis wher it is false . Salect which Above the last four columns of the folowing toble arg fout pieses of the mein tigure shown prevloushy ot the four piecas of the main figure deplets the area ündet ond of the ssimpling o Chapter 15 Problem Set each of these events, select the value, expressed in a and B, in the second column that matches the probability of that event. Recall that a is the probability of a Type I error, that is, rejecting the null hypothesis when it is true. Bi the probability of a Type II error, that is, not rejecting the null hypothesis when it is false. Above the last four columns of the following table are four pieces of the main figure shown previously. Select which of the four pieces of the main figure depicts the area under one of the sampling distributions that corresponds to the probability of the event described. (Note: The pieces depicted may not be the same size as they are in the figure. Match the pieces to the originals by color and/or pattern and labels.) Probability Value μο μα Rejecting Ho when it's true Not rejecting Ho when it's true Rejecting Ho when it's false Not rejecting He when it's false Power when Ho is false Suppose you keep the level of significance end gverything else eg same) but your value of ua in the alternative hypothesis is higher than its valug in the original figure. ppens to each of the probablities? (Hint: It may elp to redraw the figure yoursel Suppose you keep the level of significance and everything else the same, but your value of ua in the alternative hypothesis is higher than its value in the original figure. What happens to each of the probabilities? (Hint: It may help to redraw the figure yourself.) Probability Rejecting Ho when it's true Not rejecting Ho when it's trueO Rejecting Ho when it's false Not rejecting Ho when it's false Power when Ho is false Increases Decreases Stays the Same 2 Now consider what would happen if instead of considering a different value of Ha, you decide to increase the level of significance a (for example. use α-.10 instead of α " .05), what happens to each of the probabilities (as compared to the original values in the first section)? (Hint: Increasing a makes it easier to reject the null hypothesis.) Probability Rejecting Ho when it's true Not rejecting Ho when it's true Rejecting Ho when it's false Not rejecting Ho when it's false Power when Ho is false Increases Decreases Stays the Same

Answer 1

ko te to be tru

luo ha be thus kn 11ん

OLWER ox tin